Complex dynamics in a delayed diffusive cell population model of hepatitis b with capsids, mitotic transmission, and non-cytopathic antiviral mechanisms

Abstract

Hepatitis B virus (HBV) infection remains one of the most serious global health challenges of our time. It causes liver diseases such as hepatocellular carcinoma, cirrhosis, and liver failure. Understanding the host-virus interactions involved in the pathogenesis of HBV is crucial for designing more effective preventive and therapeutic strategies. In this paper, we investigate the viral dynamics of an HBV mathematical model governed by partial differential equations (PDEs), incorporating mitotic transmission, the cure of infected hepatocytes, a saturated infection functional response rate, HBV DNA-containing capsids, and three distinct delays representing intracellular delay, intracellular capsid production delay, and virus replication delay. We establish the existence, uniqueness, positivity, and uniform boundedness of solutions. By conducting a qualitative analysis and employing Lyapunov functionals, we study the global asymptotic stability of both the infection-free equilibrium and the unique endemic equilibrium under suitable conditions and threshold parameters. Furthermore, we perform numerical simulations, utilizing biologically relevant parameter values, to illustrate the analytical results and to demonstrate the model's capability to provide deeper insights into HBV infection dynamics. Our findings reveal rich and complex patterns, including both regular and irregular periodic oscillations. Notably, irregular oscillations may indicate disruptions in hepatocyte regulation and subsequent deterioration of functional activity. A comparison with existing models in the literature highlights that our model avoids the overestimations present in models that neglect certain compartments and delays